ALBERT

Notes: The libron–phonon coupling (LPC) model is used to calculate the IR absorption coefficient of diatomic molecules trapped in solid matrices at low temperatures. The coupling between the collective motions of the crystal and the molecule libration-type motion is at the basis of the LPC model. This coupling results in temperature dependent shifts and broadening of the spectral lines even in the low temperature regime. The near IR experimental spectra of CO in Ne, Ar, Kr, and Xe matrices are successfully interpreted with the present theory. The strength of the libron–phonon coupling and other constants pertaining to the theory are reported. The far IR spectra is predicted as well.

Notes: Ultraviolet absorption cross sections of ν3 vibration-excited UF6 molecules were measured in the wavelength region between 230 and 280 nm. The state-selective excitation was accomplished by 16 μm laser pumping of the ground vibrational state of flow-cooled UF6. Maximum changes in the absorption cross sections were observed toward longer wavelengths in the wings of the two charge transfer bands located at 220 and 260 nm. The results are discussed in terms of a transition from the ν3 vibrationally excited state to an upper dissociative potential surface. The change in the UV absorption cross section was also monitored as a function of the IR laser frequency and the sample gas temperature. The IR excitation spectrum follows qualitatively the low resolution contour of the ν3 Q branch. The magnitude in the absorption change is dependent on the fraction of molecules being accessed by the IR laser. The characteristic relaxation time for the ν3 excitation was estimated to be about 0.25 μs Torr at 100 K.

Notes: The infrared vibration-rotation spectrum of NH− has been obtained by autodetachment spectroscopy in a coaxial laser–ion beam spectrometer. Transitions from the v=0 to v=1 vibrational levels were excited with an F-center laser, and subsequent autodetachment from the v=1 levels was observed. The apparatus resolution was better than 20 MHz, allowing the resolution of the fine structure and Λ-doubling transitions. The linewidths of the autodetachment resonances revealed some of the dynamics of the autodetachment process. The autodetachment rates were, in general, much greater for the upper Λ-doublet levels of NH−(v=1) than for the lower levels. In addition, the increase of the autodetachment rate with rotational energy for the upper levels was much faster than would be predicted if vibrational autodetachment were the primary detachment mechanism. It therefore appears that rotational-electronic coupling plays an important role in this system, and the differences in the Λ-doublet autodetachment rates are explained in terms of this mechanism.

Notes: An ability to prepare clathrate hydrates using low temperature–high vacuum techniques, originally demonstrated for the hydrate of oxirane (Bertie and Devlin), has been extended to include the structure I hydrate of H2S, the mixed structure I hydrate of oxirane and ethane, as well as the structure II simple hydrate of THF and the double hydrates of THF with oxirane and H2S. The crystalline clathrate films (∼6 μ) have been formed either by annealing amorphous host–guest deposits at ∼130 K, epitaxial growth at 110 K (oxirane and mixed ethane–oxirane), or direct deposition at 150 K (THF and its double clathrates). Use of the epitaxial approach at ∼100 K has permitted the formation of the oxirane clathrate hydrate containing intact isolated D2O molecules. This has permitted the FT–IR observation of the ν3–ν1 doublet in the O–D stretching region (2455 and 2380 cm−1 at 100 K) with the values, after correction for Fermi resonance, suggesting a splitting from intramolecular coupling of ∼56 cm−1 (2455 vs 2399 cm−1), which compares closely with the 52 cm−1 deduced for cubic ice. Spectra for the structure I hydrates of oxirane and H2S contain absorption bands produced by guest molecules confined to both small and large clathrate cages. Use of the structure II double hydrates has permitted the firm identification of the structure I infrared bands with oxirane and H2S molecules in cages of one size or the other. Thus, the weaker ν3 and (ν11,ν14) bands of oxirane at 1281 and 1152 cm−1 have been assigned to molecules in the small cages since only these oxirane features remain in the structure II double hydrate with THF. In this case the smaller oxirane molecules occupy the small cages while the THF molecules enter the larger cages, exclusively. In a similar manner, the H–S stretching vibrations of H2S in the structure I small cages have been assigned to a band complex near 2610 cm−1, some 50 cm−1 above the band system for H2S in the large structure I clathrate cages.Such a result suggests that the net H2S perturbation, relative to the gas phase, is greater for the large than for the small cages and may be interpreted as evidence for a "double well'' large cage potential or as further evidence that the cage model of Pimentel and Charles for guest-molecule stretching modes is valid.

Notes: A critical analysis is given of the EPR spectrum exhibited by the rare-earth S-state ions, Gd3+ and Eu2+, in glassy and disordered polycrystalline materials. The analysis of this spectrum and of its previous interpretations is based on (a) a set of criteria derived from a wide range of experimental EPR and optical data, and (b) a first principles computer simulation method which explicitly incorporates broad distributions in the crystal field interaction parameters. It is found that all four previous interpretations of the glassy spectrum are unsatisfactory, each failing to satisfy two or more of the criteria imposed by the full range of data. The correct general solution to the spectrum is unequivocally established and shown to be a convolution of (a) a broad and essentially unimodal distribution of second-order crystal field parameters, b02, with a maximum in the approximate range 0.051(approximately-less-than)b02 (approximately-less-than)0.056 cm−1, and (b) a broad distribution of asymmetry parameters, λ'=b22/b02, with appreciable probability over the whole range 0.0≤ λ'≤1.0. The prominent features in the X-band spectrum at g∼6.0 and 2.8 are found to be the result of specific EPR transitions that are stationary with respect to b02, λ', and the orientation angles of the applied field H over a wide range. The quantitive results indicate that the site symmetries of the RE ions are essentially very low and disordered, and are best characterized by a single low-symmetry "glassy type'' site.

Notes: Convergent renormalized perturbation series for the Stark rotational energies of rigid polar diatomic molecules are presented. The small- and large-field expansions are considered and convergence for all field intensities is proved in both cases. Results are in excellent agreement with accurate numerical non- perturbative calculations.

Notes: Quantum and semiclassical energies are compared as a function of anharmonicity using the Hecht Hamiltonian for the triply degenerate anharmonic oscillator for octahedral and tetrahedral molecules. Semiclassical energies are found by turning on the potential adiabatically and the corresponding classical trajectories are described in terms of an adiabatic vibrational energy (VE) surface. Accurate semiclassical energies are obtained for chaotic trajectories near the separatrix of the VE surface. The quantum wave functions corresponding to the semiclassical trajectories after the onset of chaos are used to disprove a recently proposed quantum analog to classical quasiperiodic motion.

Notes: A diagrammatic representation for the chain elements in the tridiagonal representation of a Hamiltonian is developed for the mutliphoton excitation of a molecular active mode which is coupled to a background of radiatively inactive modes. Both harmonic and anharmonic models for the active mode are discussed. Statistical level congestion of the background modes is discussed and we show the relative importance of various diagrammatic paths for both strong and weak laser intensities.

Notes: Selenium reacts with fluorine with a weak visible chemiluminescence between 3800 and 8900 A(ring). Identical spectra are obtained regardless of whether the source of selenium is the elemental vapor or hydrogen selenide. By analogy with C10, TeF, and reevaluated SF absorption data, the SeF band system is assigned to transitions between inverted 2Π states. The spectroscopic constants for the A 2Π3/2 to X 2Π3/2 system are: Te=14 680.4 cm−1, ω‘e =688.8 cm−1, ωex‘e =1.84 cm−1, ω'e =444.1 cm−1, and ωexe =2.93 cm−1. The weak 2Π1/2 to 2Π1/2 subband is described by the constants: Te =15 025.4 cm−1, ω‘e =683.0 cm−1, ωex‘e =2.11 cm−1, ω'e =436.9 cm−1, and ωexe =1.20 cm−1. Laser excitation spectra were recorded for the SeF chemiluminescence flame. The SeF fluorescence between 4200 and 5200 A(ring) is rapidly quenched with increasing total pressure. A Stern–Volmer analysis gave a zero pressure lifetime of 12.8±3.9 μs. The measured quenching rate of 2.5×106 s−1 Torr−1 is nearly gas kinetic.

Notes: Electronegative substituents such as F favor closed-shell singlet, while electropositive substituents such as Li favor triplet ground electronic states in carbenes and silylenes. Therefore, SiLiF presents a very instructive case study of the competing electronic effects involved. We have examined the minima on the lowest-lying 1A', 1A‘, and 3A‘ potential surfaces of SiLiF, using self-consistent-field and configuration interaction methods with a basis set at the double zeta plus polarization level. Two minima, one with a wide and the other with a narrow bond angle θ (LiSiF), have been found for each of the three electronic states, in analogy with SiHLi. The most stable minimum at all levels of approximation is the narrow-angle triplet (3A‘ I). It lies below the second most stable minimum, the narrow-angle closed-shell singlet (1A' I), by 10.5 kcal/mol at the CISD level of theory. This result is similar to the singlet–triplet separation in SiHLi at the same level of theory (10.7 kcal/mol), demonstrating that the electropositive Li atom prevails against the electronegative F. The harmonic vibrational frequencies and the results of a Mulliken population analysis are also presented for each minimum.

Notes: Potential energy and dipole moment functions for the ground states of SH, SH+, and SH− have been calculated from highly correlated electronic wave functions. The electric dipole moments in the vibrational ground states of 32SH, 32SH+, and 32SH− are calculated to be 0.74, 1.29, and 0.27 D, and the rotationless rates of spontaneous emission A10 to be 1, 52, and 75 s−1, respectively. The predicted transition probabilities between the low lying vibrational states of the electronic ground state of SH and SD are among the smallest so far known for dipole allowed rotation-vibration transitions. The calculated A–X transition probabilities in SH confirm recent indirect determinations of the radiative lifetimes and absorption oscillator strengths in the predissociating v'=0 level of the A state. The 4Σ− state is calculated to intersect the A 2Σ+ state at R=3.1 a.u., between the classical turning points of v'=0 and 1 in the A state.

Notes: The viscosities of suspensions of sterically stabilized (hard) silica spheres in cyclohexane are reported as a function of shear rate (γ(overdot)) and volume fraction (6×10−4〈φ〈0.6). The shear thinning scales according to (ηr−η∞)/(η0−η∞) =1/(1+1.31ηγ(overdot)a3/kT) with limiting low and high shear viscosities described up to φ∼0.35 by η0=1+5/2φ+(4±2)φ2+(42±10)φ3 , η∞=1+5/2φ+(4±2)φ2+(25±7)φ3 . At higher volume fractions the viscosity becomes more sensitive to φ and diverges at φm=0.63±0.02 (γ(overdot)→0) , φm=0.70±0.02 (γ(overdot)→∞) . The experimental results compare well with existing hard sphere theories and the data of Krieger (1972) for aqueous lattices. Even at the highest volume fraction neither yield stresses nor shear thickening are observed.

Notes: A recently developed Green's function method for the calculation of molecular doubly ionized states is presented. Calculations of the dicationic states of water have been carried out, employing a number of different basis sets. For comparison, several configuration interaction calculations including multireference treatments have also been performed, complementing those available in the literature. The Green's function approach is very efficient computationally and size-consistent, therefore it appears very promising in view of its applicability to larger molecular systems.

Notes: Diffusion-controlled coarsening (Ostwald ripening) of a precipitate is analyzed for the case of an open system, immersed in a reservoir of constant solute concentration. Equivalence of the evolution of such open systems and closed systems studied previously is established in the limit of infinite systems. The cause of this equivalence is screening of the bulk of the system from the reservoir by diffusive interactions between the precipitated particles. The applicability to large, but finite systems is discussed.

Notes: A theory of line shape for a Doppler broadened probe in the presence of a strong infrared pump is presented. The optical analog of Bloch equations has been developed; the T1, T2 relaxations are introduced phenomenologically in these equations. Doppler broadening of both the pump and signal transitions are taken into account to obtain the absorption coefficient for the signal. This leads to a Doppler broadened Gaussian function weighted by a pump induced Lorentzian function whose position and linewidth are controlled by the detuning and power respectively of the pump radiation. The absorption coefficient is further modulated by a Lorentzian function containing the fourth power of the radiation. The off-resonance pumping leads to two symmetrically located "Lamb dips'' or "peaks'' around the Gaussian pedestal for co- and counter propagating laser radiations. A calculation of the line shape of the central sub-Doppler feature for the on-resonance pumping is in good agreement with the observed variation of linewidth with pressure. Numerical results are presented graphically to demonstrate the pump and signal power dependence of the central hole or peak for the bent and cascade-type double resonances. The results obtained confirm the expected behavior based on level populations.

Notes: We present a new water dimer potential. It is based on carrying out Morokuma component analyses at the ab initio level on 229 water dimer geometries and fitting the energy components to analytical functional forms. To these are then added a dispersion contribution, based on the analytical dispersion energy expression of Douketis et al. (Ref. 1). This potential gives a satisfactory description of the water dimer, with minimum R(O ⋅ ⋅ ⋅ O)=2.96 A(ring), ΔE=−5.2 kcal/mol, and minimum energy θ angle between H-bond donor and acceptor axis of 55°, in good agreement with experimental values of 2.98±0.04 A(ring), −5.4±0.2 kcal/mol, and 60±10°, respectively. The second virial coefficient B is also calculated in reasonable agreement with experiment, e.g., at 423 K, B (calculated) =−352, compared to B (experimental)=−332 cc/mol.

Notes: The spherically averaged momentum densities Π¯(p) for the ground states of the 92 neutral atoms from hydrogen to uranium, and of the 73 singly positive ions from helium to barium and from lutetium to radium, constructed from nonrelativistic SCF wave functions, are examined. From these investigations, it is noted that the general shape of Π¯(p) of an atomic system is clearly determined by the orbitals of the two outermost shells. Two distinct types of maxima that make Π¯(p) nonmonotonic have been investigated: (i) a slow type, which typically occurs for pε(0.0,0.6](h-dash-bar)a−10, and (ii) a fast type, not previously reported in the literature, which either is very small and barely noticeable, or is huge (as compared to those of the slow type), and which occurs for pε[0.7, 1.6](h-dash-bar)a−10 . The results indicate that while maxima of the slow type result from occupied p orbitals of the outermost shell when that shell possesses no occupied d orbitals, maxima of the fast type are the result of both d and p occupied orbitals.

Notes: The rate constant kd and its temperature dependence for thermal electron detachment from the azulene negative ion Az−(arrow-right-and-left)ad Az+e was determined by observing, at suitably high temperature, the decay of Az− with time. A pulsed electron beam, high ion source pressure mass spectrometer was used. The reaction mixtures typically contained 4 Torr CH4 as bath gas and azulene and perfluoromethylcyclohexane (C7F14) at pressures of a few mTorr. The C7F14 which has a large electron attachment coefficient was used as electron scavenger in order to suppress the (re)attachment of electrons to Az. The experimental data points for kd could be fitted equally well with the expressions kd =2.5×106 T3/2 (s−1)exp[−14.5 (kcal/mol)/RT] and kd =1.14×1011 (s−1)exp[−15.7 (kcal/mol)/RT]. The activation energies are close to the electron affinity E.A.(Az)=16 kcal/mol obtained in earlier determination from this laboratory. Consistent values for the equilibrium constant K of the attachment–detachment equilibrium can be obtained when K is evaluated from E.A.(Az) and third law entropies of the reactants and from K=ka/kd, where ka and kd are experimentally determined quantities. The ka values were taken from Christophorou.

Notes: Application of the harmonic oscillator cell model (HOCM) for condensed phase isotope effects to the benzene/deuterobenzene system using temperature dependent force fields, which yield good calculated values for vapor pressure isotope effects (VPIE) and reasonable agreement with spectroscopically observed frequency shifts on condensation, gives calculated values of isotope effect on energies of vaporization which are not in agreement with experiment. Pseudoharmonic corrections are inadequate to restore agreement with experiment. The VPIE in benzene is dominated by the contributions of the CH/CD stretching vibrations and consistency is achieved by expanding the model to include anharmonic corrections for these frequencies. In this fashion a combination of thermodynamic measurements of free energies (by vapor pressure) and energies (from the temperature coefficient of the vapor pressure or from calorimetry) can be employed to yield shifts in anharmonic vibrational constants on condensation. In the second part of the paper the molar volume isotope effect (MVIE) and the effects of volume, pressure, and temperature on the internal energy and its isotope effects (as monitored by the expansivity, compressibility, heat capacity, and their derivatives) are interpreted. The low-lying lattice modes make important contributions to these properties.

Notes: Proton NMR relaxation in paramagnetic systems of S=3/2 with electron spin relaxation in slow-motional region is examined. The proton relaxations arising from the modulations of scalar, dipolar, and scalar–dipolar cross interactions from paramagnetic spin by slow molecular motion together with their field dependence, the variation of zero field splitting (zfs) interaction, and internal rotation interference are investigated. The overall reorientational motion of the complex presumably gives rise to the fluctuation of zfs interaction. The model for independent modulations of dipolar and zfs interactions is considered also. The proton relaxation rates are directly calculated from the approach of solving stochastic Liouville equation for slow-motional ESR relaxations. Slow-motional effects on individual proton relaxation rates are discussed. The final results are appropriately modified to incorporate the influence of internal rotation for proton. The field-dependent methyl proton relaxation rates in tris-acetylacetonatochromium (III) complex are calculated. Effects due to various potential barriers in the internal rotation are also presented.

Notes: The chain conformational space renormalization group method is extended to consider excluded volume effects in polymer chains interacting with surfaces. The general theory is illustrated primarily by considering a system with a single impenetrable flat interface. The presence of boundaries, while breaking the translational invariance of the full-space theory, introduces a number of novel theoretical features into the renormalization group treatment. A parameter δ is introduced to describe the strength of the polymer chain–surface interaction, and previous expansions in powers of δ or δ−1 are not required. We evaluate several moments of the end-vector distribution such as 〈zn〉, 〈||ρ||2〉, etc. to first order in the excluded volume. Our work differs essentially from previous studies because the full dependence on the polymer–surface interaction parameter δ is retained to all orders, the crossover dependence on excluded volume is incorporated and the generalized crossover (i.e., excluded volume dependent) exponents are corrected through second order. Previous results, such as power law exponents, scaling forms for distributions, end-vector distributions in the absence of excluded volume, etc., are obtained simply as particular limiting cases upon the values of the excluded volume and the interaction parameter δ.

Notes: Three tunable lasers are used to perform site selective coherent anti-Stokes Raman (CARS) spectroscopy in pentacene:p-terphenyl crystals at 2 K. The vibrational and vibronic levels of pentacene in the individual substitutional sites of p-terphenyl can be selectively examined by matching the resonances of a particular site. The signals from a site and the selectivity between sites are much higher than CARS performed with two tunable lasers. The spectra are dominated by lines from processes where the vibrational and vibronic states involved in the four-wave mixing are associated with the same molecular mode. There are also important lines from processes where different vibrational and vibronic modes are involved in the nonlinear mixing. The intensities of lines from the resonant site are strongly dependent on the laser energy because of saturation of the electronic transition.

Notes: Three tunable lasers are used to generate a fully resonant nonparametric process that generates new coherent output at a higher energy than fluorescence interference in condensed phase molecular systems. The pentacene:p-terphenyl system is used as a model to test the basic ideas of the method and to compare the results with comparable spectra obtained with a parametric process. The resonance enhancement is shown to reflect intermode coupling between different vibrational and vibronic modes. Interference is observed between transitions of different pentacene sites that reflects the differences in the parametric and nonparametric processes. These differences become the dominant characteristic determining the potential for four-wave nonlinear mixing methods to provide resolution within inhomogeneously broadened electronic bands.

Notes: When the products of the reaction between F atoms formed in a microwave discharge and CH3Cl, CH3Br, or CH3I were frozen in a large excess of argon at 14 K, the infrared spectra of the primary reaction products were obtained. Isotopic substitution experiments have provided evidence for two major reaction channels in each of these three reaction systems. Attack of the F atom at the halogen position results in the formation of the CH3XF addition product, which has a moderately strong X–F bond and is photochemically stable at wavelengths as short as 250 nm. F-atom reaction with a hydrogen atom of the methyl halide results in the stabilization of a weakly bound F⋅⋅⋅HCH2X complex, intermediate to the formation of H2CX+HF. For all of the species studied except CH3Cl, the barrier to the decomposition of this complex is sufficiently great to require exposure of the solid deposit to visible light for the production of H2CX and HF. The infrared spectra of the H2CX⋅⋅⋅HF hydrogen-bonded complexes isolated in solid argon are discussed.

Notes: In a recent paper, Hardwick predicted that the optical spectrum of NO2 should display "quantum ergodicity'', meaning that almost all eigenstates allowed by total symmetry should be seen in absorption. We have performed a test of this prediction by using the technique of microwave detected, microwave–optical double resonance. We have determined the spectrum over the range 16 810–17 100 cm−1 for the two ground vibrational states 91,9(F1) and 100,10(F1) of NO2. We observed 324 transitions from the 100,10 state and 364 transitions from the 91,9 state. The number of observed transitions is a factor of 8 greater than that expected if only the allowed rotational transitions to any B2 symmetry vibronic level were observed. The number of observed lines is a factor of 3 less than the number predicted if all selection rules were broken as predicted by Hardwick. Thus we see that Hardwick's "ergodicity'' conjecture is a useful starting point for understanding the spectrum of NO2, but the spectrum is intermediate between the regular and the ergodic limits.

Notes: We present the theoretical framework necessary to describe inelastic collisions between Stark mixed Λ-doublet levels of a molecule in a 1Π electronic state, and the subsequent effect on fluorescence intensities. It is convenient to work with the spherical tensor moments of the excited state density matrix. For weak fields and short times after excitation the ratio of the fluorescence intensities for emission on "forbidden'' and allowed 1Σ+←1Π lines is predicted to vary linearly with time and quadratically with field strength. Simulation studies are presented, based on collisional parameters suggested by previous theoretical studies of inelastic collisions of molecules in Π electronic states. The present article provides the foundation for the accurate interpretation of laser diagnostic studies in plasma environments, such as those described by Mandich, Gaebe, and Gottscho in the accompanying article.

Notes: We describe time-resolved and spectrally resolved laser-induced fluorescence measurements from the parity or Λ doublet levels of the A 1Π state of BCl radicals formed by CO2 laser multiphoton dissociation of BCl3 molecules. We show how the effects of collisional mixing can be discerned from the effects of electric field mixing. A set of rate equations for population transfer which include the effects of both field and collisional mixing under conditions of incoherent excitation are derived and compared to the more general theory of Alexander. Zero-field measurements of collisional mixing rates yield parity-changing rate constants kef whose rotational quantum number J dependence is consistent with a dipole–induced-dipole collision model: kef=3.4, 2.6, 1.9, and 1.4×106 s−1 Torr−1 for J=3, 5, 11, and 18, respectively. Measurement of time-resolved fluorescence from Stark mixed parity levels in the presence of a strong electric field indicates that the levels are prepared coherently. Time integrated measurements as a function of the applied field are used in generating empirical calibration curves for determining local field magnitudes in discharges containing BCl radicals.

Notes: This paper presents a detailed theoretical study of the NO vibration/rotation distributions produced in nonreactive H+NO collisions in the 1–3 eV range of relative translational energies. The collision dynamics is studied by applying the quasiclassical trajectory method to each of the four potential surfaces (1A', 1A‘, 3A', 3A‘) which correlate to H(2S)+NO(2Π), followed by a statistical average of the cross sections over the four surfaces. Each surface is generated by fitting a flexible empirical function (a sum of Morse functions with coordinate dependent parameters) to available ab initio and experimental data on the surfaces. The resulting vibrational distributions are in excellent agreement with measured laser induced fluorescence results at 0.95 and 2.2 eV. In addition, the average fraction of energy transferred into vibration shows the same flat dependence on translational energy in the 1–3 eV range that is seen experimentally, and which contrasts with the linear proportionality seen for the corresponding H+CO system. Details of the collisions are analyzed, and it is found that complex formation plays a much more important role in H+NO than in H+CO, with roughly 2/3 of the cross section at 0.95 eV and 1/5 that at 2.2 eV due to complex formation. In fact, at both energies, the trajectory vibrational distributions are quite close to statistical. At 2.2 eV, however, direct collisions make a substantial contribution to the vibrational excitation process, so the agreement with statistical theory is partly accidental. The rotational distributions are found to be substantially colder than statistical, particularly at higher energy, with an average rotational quantum number which is independent of vibrational state except for the highest three states allowed by energy conservation. Agreement between experimental and theoretical rotational distributions is poorer than for the vibrational distributions, with the theoretical rotational distributions being hotter. This presumably reflects errors in the anisotropy of the potential energy surfaces.

Notes: The possibility of designing pulse sequences to select NMR responses from spin systems of a given coupling topology is examined. The selection can be achieved by topology-selective multiple-quantum excitation sequences. The performance of some pulse sequences for exciting high-order multiple-quantum coherences is analyzed and verified experimentally. Treatment is given of the measurement of the intensity of multiple-quantum coherence, the sensitivity and specificity of topology-selective multiple-quantum experiments, and of the relationship between these pulse sequences and "spin editing'' methods in heteronuclear NMR. A scheme for general compensation of pulse errors is also described. Practical application of spin topology filtration to two-dimensional NMR of a small protein is demonstrated.

Notes: We have calculated the phase diagram of coexisting liquid and solid adhesive hard spheres, using the modern density functional theory. The predicted phase diagram displays many of the observed experimental trends in the freezing of simple substances. It also has unusual features, such as a "reentrant'' liquid phase at certain densities. We have also identified distinct metastable solids at low temperature.

Notes: The dynamics of the cluster–cluster aggregation process is investigated through the time dependent cluster size distribution function using Monte Carlo simulations, scaling theory, and the Smoluchowski coagulation equation. Depending on such factors as the chemical reactivity, kinetic energy, mass, etc. of the aggregates the coagulation of two clusters may or may not take place. These effects are simulated by assuming that the probability that two clusters of sizes i and j irreversibly stick together is proportional to (ij)σ. Our results show that for constant small sticking probability cluster size distribution and its moments asymptotically scale with the same exponents as for the case when the sticking probability is unity. In the early stages, coagulation is slow and the process is chemically controlled. However, for finite sticking probability, as the aggregation process develops in time the chance that two clusters join permanently increases with the surface of the cluster and there is a crossover from chemically controlled to diffusion-limited aggregation. The effect of a finite σ is similar to the exponent γ for the mass dependent diffusion coefficient. There exists a critical value, σc, above which for a given γ the cluster size distribution changes from a bell shaped curve to a monotonically decreasing function of s, in agreement with various experiments. The simulations are found to agree with the dynamic scaling theory, but a reasonable approach to include the effect of sticking probability within the Smoluchowski equation fails to produce results that agree with the simulations.

Notes: The formation of water–ammonia binary clusters (H2O)n(NH3)mH+ (q(approximately-less-than)40, q=n+m), have been investigated employing a neutral supersonic nozzle expansion of premixed water–ammonia gas with molecular-beam-mass spectrometry. The analysis of the mass spectra reveals that the number of water-rich clusters is greatly increased as the cluster size is increased. Mass spectroscopic evidence for the existence of enhanced structural stabilities ("magic numbers'') has been found at the protonated clusters (H2O)20(NH3)mH+ (m=1–6) and (H2O)27NH+4 . Considerations for the magic number stabilities are presented within the framework of ion clathrate (ion-centered cage) structures. Monte Carlo simulations are also presented for ionized (protonated) clusters around n=20 and n=27 with m=1. The clusters (H2O)20NH+4 and (H2O)27NH+4 have greater binding energies per molecule than their neighbors, in agreement with the mass spectroscopic observations. The calculated structure for (H2O)20NH+4 also indicates the stability of pentagonal rings of water molecules and deformed dodecahedral structure with an NH+4 ion trapped inside; the cluster is especially stable due not only to the strong Coulombic interaction (ionic hydrogen bonding) between the NH+4 ion and the surrounding 20 water molecules but to hydrogen bonding networks forming the cage structure. The proposed ion-centered cage model can also explain satisfactorily the well-known stability of the water cluster of (H2O)20H3O+.

Notes: A detailed investigation of the spatially anisotropic component of the laterally averaged molecular hydrogen/Ag(111) physisorption potential is presented. Experimentally derived rotationally inelastic transition probabilities for H2, D2, and HD, taken as a function of collision energy, are compared with those resulting from close-coupled quantum scattering calculations. These calculations utilize exponential-3 and variable exponent parametrizations of the laterally averaged isotropic potential which reproduce the experimental bound state resonance spectra for p-H2 and o-D2 on Ag(111). Complementary information is obtained by analyzing the magnetic sublevel splittings for physisorbed J=1 n-H2, using diffractive selective adsorption resonance energies calculated with first order perturbation theory. Theoretical predictions for HD/Ag(111) rotationally mediated selective adsorption resonances are also compared with previously reported experimental results, which show well resolved J-dependent energy shifts resulting in part from the orientational anisotropy of the potential. The results obtained in this study indicate that both the attractive and repulsive parts of the anisotropic potential exhibit only a weak orientation dependence, in agreement with recent theoretical predictions for this system.

Notes: A general method is described for the formation of cold metal cluser negative ion beams which serve as excellent sources for photodetachment experiments. The method involves the pulsed laser vaporization of a metal target at the throat of a pulsed supersonic helium expansion. By the optimization of source conditions, intense beams (greater than 105 ions/pulse) of both positive and negative ions are produced routinely. Ionization of the metal cluster molecules, either during vaporization or by irradiation with 193 nm light, occurs prior to supersonic expansion and produces a cold plasma entrained in the neural flow that is renitent to stray electric and magnetic fields, unlike photoions produced in the collisionless downstream molecular beam. The enhancement of the negative ion flux by 193 nm irradiation is believed to be evidence for efficient electron attachment of low energy photoelectrons generated in the nozzle region. This attachment process, however, is apparently not effective for molecules containing less than ∼4 metal atoms. Laser irradition of mass-selected cluster anions extracted from these cold ion beams reveal that photodetachment of the metal cluster negative ion is always the preferred pathway, even when fragmentation of the ion is possible. This new negative ion production technique should therefore permit measurement of both electron affinities and photoelectron spectra as a function of cluster size and composition.

Notes: The complex resonance energies (positions and widths) and wave functions for the lowest 1Σ+g doubly excited autoionizing states of H2 are directly computed by using the multiconfiguration self-consistent field (MCSCF) method and the configuration interaction (CI) method within the context of the complex basis function technique. These autoionizing states are Feshbach resonances (as opposed to shape resonances), and single-configuration self-consistent field calculations provide no information about the lifetimes of such states. All of these methods rely on the existence of a complex variational principle for complex resonance energies. It is shown that by using a small orbital space the MCSCF method can give essentially the same complex energies as the full CI method. Numerical results are in good agreement with previous theoretical results, especially with the optical potential calculation employing a diffuse basis set by Schneider and Collins [Phys. Rev. A 28, 166 (1983)], indicating that poor agreement with previous complex coordinate results by Moiseyev and Corcoran [Phys. Rev. A 20, 814 (1979)] is attributable to their small basis set. A detailed study of basis set and correlation effects on the complex energies is also presented.

Notes: Investigations of the wave vector dependence of theoretical phonon frequencies of neon, argon, krypton, and xenon, deduced by invoking a six constant Clark, Gazis, and Wallis model, reveal that they satisfy a relation, Mν2[sin(πζ/p)]n =Φ(r), a constant which depends on individual rare gas solid with p=1 or 2 and n=−2.018±0.038 at all polarizations except [110]L along the principal symmetry directions and hence their dependence on wave vector q could be separated from that on nearest neighbor distance, r. It is shown that the latter is adequately represented at all wave vectors and polarizations in the Brillouin zone by a homologous relation, Mν2rα =δ(q), a constant with α=−2.818±0.127 in the case of argon, krypton, and xenon and could be exploited to determine the zero point energy which destroys the homology in the case of neon. The physical significance of these empirical relations, the degree of homology that exists among these rare gas solids, influence of zero point energy on their dispersion relations, as well as the accuracy of scaling factors in the evaluation of zero point energy are discussed.

Notes: We derive a ten-term recursion relation that describes exactly the occupational degeneracy for indistinguishable dumbbells distributed on a hexagonal lattice space. The generating functions, normalization, expectation, dispersion, and continuous representation of the associated statistics are also treated. In addition, the occupational degeneracy at saturation is discussed.

Notes: Standard techniques of classical field theory are introduced in order to arrive at a unique definition of the pressure tensor in the thermodynamics of nonuniform fluids. We show that the familiar thermodynamic definition of the elastic stress as the derivative of the free energy with respect to strain can be used to this purpose by replacing the strain components with the components of the metric tensor as independent thermodynamic variables. As an application we calculate the pressure tensor in the case that the free energy is known as a local functional of the one particle density and, in the square gradient approximation, confirm Lovett expression. Moreover, the mechanical expression for the surface tension is obtained from the elementary thermodynamic definition; a scalar pressure is defined and shown to have a weak singularity at the critical point as expected; finally a modified Euler hydrodynamic equation is introduced.

Notes: The action of light on undersaturated and supersaturated vapors of carbon disulfide has been investigated using a batch photochemical reactor and a thermal diffusion cloud chamber, respectively. Photoinduced nucleation was observed in each case. In the batch reactor enough sulfur was produced to nucleate and grow a sulfur aerosol. A model for the photoinduced nucleation of supersaturated carbon disulfide is proposed based upon the photochemical production and subsequent nucleation of sulfur. The model predictions compare well with observed nucleation delay time and nucleation rate data. A variation of the model utilizing diradical polymerization instead of nucleation is used to explain photoinduced nucleation results in the literature involving dilute solutions of carbon disulfide in supersaturated ethanol vapor.

Notes: The first infrared spectra of protonated hydrogen clusters in the gas phase have been observed. Predissociation spectra were taken with a tandem mass spectrometer: mass selected hydrogen cluster ions were irradiated inside a rf ion trap by a tunable infrared laser, and the fragment ions created by photodissociation of the clusters were mass selected and detected. Spectra for each product channel were measured by counting fragment ions as a function of laser frequency. Low resolution spectra (Δν=10 cm−1) in the region from 3800 to 4200 cm−1 were observed for the ions H+5, H+7, and H+9 at 3910, 3980, and 4020 cm−1, respectively. A band was also observed for H+5 at 3532 cm−1. No rotational structure was resolved. The frequencies of the band maxima agree well with the frequencies predicted by previous ab initio calculations for the highest modes.

Notes: It will be demonstrated that the chemical shift anisotropy (CSA) relaxation mechanism for protonated aromatic 13C nuclei is by no means negligible. The cross correlation spectral density arising from dipolar and CSA interactions in the natural abundance 13C–H spin system of pentachlorobenzene is included in the complete determination of the molecular motional anisotropy. Additionally, the absolute sign of the indirect coupling constant 1JCH is shown to be positive.

Notes: We present an accurate and efficient method for EBK quantization of bound states in multidimensional systems, based upon a Fourier representation of invariant tori in the quasiperiodic regime. The key feature of the method is the direct determination of good action variables from Fourier transforms of trajectories, using a formula due to Percival. It is possible to calculate actions using this formula provided frequencies and Fourier components can be determined to high accuracy. We describe a special windowing technique for this purpose, which overcomes the stability problems encountered in the recent related work of Eaker, Schatz, De Leon and Heller. Quantized energy levels can be found either by direct search for quantizing trajectories or by linear extrapolation from nearby arbitrary tori. Results are presented for two-, three-, and four-dimensional vibrational Hamiltonians.

Notes: We develop methodology for performing time dependent quantum mechanical calculations by representing the wave function as a sum of Gaussian wave packets (GWP) each characterized by a set of parameters such as width, position, momentum, and phase. The problem of computing the time evolution of the wave function is thus reduced to that of finding the time evolution of the parameters in the Gaussians. This parameter motion is determined by minimizing the error made by replacing the exact wave function in the time dependent Schrödinger equation with its Gaussian representation approximant. This leads to first order differential equations for the time dependence of the parameters, and those describing the packet position and the momentum of each packet have some resemblance with the classical equations of motion. The paper studies numerically the strategy needed to achieve the best GWP representation of time dependent processes. The issues discussed are the representation of the initial wave function, the numerical stability and the solution of the differential equations giving the evolution of the parameters, and the analysis of the final wave function. Extensive comparisons are made with an approximate method which assumes that the Gaussians are independent and their width is smaller than the length scale over which the potential changes. This approximation greatly simplifies the calculations and has the advantage of a greater resemblance to classical mechanics, thus being more intuitive. We find, however, that its range of applications is limited to problems involving localized degrees of freedom that participate in the dynamic process for a very short time. Finally we give particular attention to the notion that the GWP representation of the wave function reduces the dynamics of one quantum degree of freedom to that of a set of pseudoparticles (each represented by one packet) moving according to a pseudoclassical (i.e., classical-like) mechanics whose "phase space'' is described by a position and momentum as well as a complex phase and width.

Notes: An analysis of internal particle equilibrium in J. Chem. Phys. 81, 2489 (1984) is generalized by means of Lagrange's method of undetermined multipliers to show that a one-component crystalline particle of fixed size and shape is at equilibrium at constant temperature and pressure when the chemical potentials of molecular species, μi, μj, ..., and of vacancies μvi, μvj, ..., for sites i, j,... of different characteristic bond environments fit the relation μi−μvi=μj−μvj =⋅⋅⋅ . The chemical potential differences between molecular species and vacancies is shown to be the chemical potential for the component. The influence of surfaces on vapor pressures is predicted by setting the chemical potential of the component in the particle equal to that of its vapor. The predicted effects of surfaces are larger than those of classical theory but are in reasonable agreement with measurements for liquid drops.

Notes: The autocorrelation functions of second order generalized harmonics for the restricted librational motion of a spheroid were calculated using a wobbling-in-a-cone model. The model represents a motion intuitively abstracted from the multiple internal rotations of a side chain or the anisotropic libration of backbone segments in macromolecules. The exact correlation functions expressed by multiexponential decay were found well approximated by a single exponential decay where integrated areas of the exact and approximated functions were taken to be the same. The results were used to express the relaxation of nuclear spins caused by the fluctuation of the dipole–dipole interaction. The multiexponential nature of exact correlation functions was related to the concept of the relaxation spectrum.

Notes: Formulas for the calculation of the 13C NMR chemical shift of infinite polymer chains were derived by the tight-binding theory within the CNDO/2 framework incorporated with the sum-over-state method. This formalism was applied to the calculation of the 13C NMR chemical shift tensor of polyethylene and cis and trans polyacetylenes. The calculated results were found to agree with the experimental data.

Notes: Several reactions of the form A+HD→AD(H)+H(D) have been studied by a two laser experiment. One laser dissociates a molecule to form a reactive atom A and the second laser monitors the hydrogen atom products by laser induced fluorescence. When A is F(2P), O(1D), and S(1D), the H/D ratios are 0.66±0.10, 1.13±0.08, and 1.91±0.10, respectively. Muckerman and co-workers have given qualitative arguments that abstraction reactions should have an H/D ratio less than one whereas insertion reactions should have H/D greater than one. Inasmuch as extensive previous experimental and theoretical work has shown that F(2P)+H2 procedes by abstraction whereas O(1D)+H2 and S(1D)+H2 proceed largely by insertion, the present results are consistent with the general qualitative conjecture.

Notes: The reaction of hydrogen atoms with NF2 was studied in a flow tube using pulsed KrF laser initiation of H2/NF2/Ar mixtures at 440 K. The quantum yield for NF(a) production from the 249 nm photolysis of NF2 was determined to be 0.10±0.05. Several important reactions in this system were investigated, and rate coefficients were determined at 440 K. A value of (1.03±0.20)×10−30 cm6/molecule2 s was obtained for the three-body recombination of F atoms with NF2 and Ar. Rate constants for the relaxation of HF(v=2) and HF(v=3) by NF2 are (9.7±1.0)×10−14 and (2.5±0.5)×10−13 cm3/molecule s, respectively. Study of the quenching of NF(a) by NF2 yields a rate coefficient of (2.7±1.0)×10−16 cm3/molecule s. Evidence is presented that indicates the disproportionation of NF(a) is three orders of magnitude slower than that of ground state NF. Modeling results are presented which agree well with experimental data.

Notes: A solution to the Kramers equation for the kinetics of the trans–gauche isomerization of n-butane in CCl4 is obtained in terms of the expansion of the probability density function in the eigenfunctions of the Kramers operator. The eigenfunctions. and corresponding eigenvalues are determined with the expansion in a basis set composed of Hermite polynomials in speed and the eigenfunctions of the Smoluchowski operator in the spatial coordinate. The Smoluchowski equation describes the situation when the speed variable is distributed in accordance with the equilibrium Maxwell–Boltzmann distribution and is the high collision frequency limit of the Kramers equation. The range of validity of the first order kinetics is examined in terms of the nature of the eigenvalue spectrum of the Kramers operator. The rate coefficient is determined in terms of the smallest nonzero real eigenvalue and comparisons are made with the results of other researchers.

Notes: A simple model study of laser induced transitions between electronic surfaces in reactive molecular collisions has been undertaken. The investigation is characterized by laser and nonadiabatic couplings which are turned on during the course of a collision. Transition probabilities are determined within an exact quantum-mechanical framework, for switching between the model one-dimensional potential curves as a function of various system parameters. Such parameters include the photon energy, the reactant collision energy, and the coordinate separation between the positions of potential barrier maxima. The processes studied involve not only laser switching but, also, cooperative laser and nonadiabatic effects. A number of features of the results are emphasized.

Notes: An expression for the microcanonical rate constant that can be conveniently evaluated by path integral techniques is proposed. The efficacy of the method is illustrated by obtaining accurate transmission probabilities as a function of energy for a particle tunneling through an Eckart barrier. The application of the method to systems involving many degrees of freedom is discussed.

Notes: New upper and lower bounds to the van der Waals C6, C8, and C10 coefficients for hydrogen, noble gas, alkali, and alkaline earth atoms are determined by using Padé approximants to bound the dynamic multipole polarizabilities. Also, the nonadditive, three-body coefficients involving dipole, quadrupole, and octupole interactions are bounded.

Notes: A Monte Carlo simulation of an electron in a hard sphere fluid is described. Five thermodynamic states along the isotherm λ=6σ have been examined (λ is the thermal wavelength of the electron, σ is the diameter of a sphere, d=σ/2 is taken as the distance of closest approach between a sphere and the electron). At fluid densities below 0.2σ−3, the electron fluctuates in extended configurations. At higher densities, we find that the fluid of random scatterers localizes the electronic configurations into compact yet fluctuating structures occupying voids in the fluid. Between the densities 0.1 to 0.2σ−3 we observe two relatively stable yet distinct electronic structures, one compact and the other extended. This observation of apparent metastable states seems to imply nonlinearities in the fluctuations of the electron suggestive of phase transition behavior. The statistics of the fluctuations in the compact structures are in perfect agreement with earlier results obtained for an electron in rigid disordered array of scatterers. The results of the simulation for both extended and localized states are compared with those obtained from the integral equation theory of Chandler et al. The Monte Carlo calculations were made possible by the use of the staging algorithm. This renormalization procedure allows for the efficient sampling of electronic and fluid fluctuations that extend over many length scales. The competition between the variety of length scales is intrinsic to the physics of the solvated electron.

Notes: The Hilbert solution of the Boltzmann equation for a multiple gas mixture is presented. It is shown that the first approximation of the Hilbert theory yields the Euler equations for ideal flow. The Hilbert field equations of the second approximation are derived and the transport processes that appear in this approximation are discussed in a manner similar to that given in Chapman and Cowling. The Hilbert formulas for the transport coefficients of a multiple gas mixture are obtained and are seen to be precisely the same formulas of Chapman and Cowling obtained by the Chapman–Enskog method.

Notes: A Monte Carlo simulation of a solution of 1,2-dichloroethane in methyl chloride has been performed in the NPT ensemble. The solution serves as a model to study the differential solvation of the gauche and anti conformers of a polar solute in a polar solvent. The expected conformational change induced by the solvation in favor of the gauche conformer is well reproduced in the simulation. To explain it, the r−12, r−6, and r−1 contributions of the intermolecular potential functions (TIPS format) to the solute–solvent and solvent–solvent energies have been recorded during the simulation. The mean r−1 contributions are computed to be less than one-third of the sum of the r−12 and r−6 contributions; however, the computed difference of 2±0.5 kcal/mol between the gauche and anti solute–solvent mean energy is totally accounted for by the difference in the r−1 contributions. The analysis of the r−1 energy pair distribution shows that the main part of this difference comes from changes in the interaction of the solute with the nearest solvent neighbors. The gauche conformer shows at one and the same time more attractive and more repulsive interactions than the anti conformer. When the pure liquid, the anti and gauche solutions are compared, it is found that the solvent molecules experience, on the mean, nearly the same solvent–solvent interactions in the three cases.

Notes: The results of the application of sensitivity analysis to the simulation of gas–surface scattering are presented. The simulation technique was the three dimensional generalized Langevin method of Tully, and the sensitivity analysis methods were the coupled solution of system and sensitivity equations approach and a new stochastic sensitivity analysis method. We found that the coupled solution approach only converged when trajectories which involved multiple collisions of the gas with the surface were excluded from the Monte Carlo averaging of this simulation approach. The stochastic sensitivity method was found to give convergent results for both single collision trajectories and multiple collision trajectories. In the stochastic sensitivity method the sensitivity coefficients are computed by selecting the parameters of the system randomly from a given distribution and then performing a linear least-squares analysis of the variations of the output variables of the simulation model with respect to variations of the input parameters. The stochastic sensitivity analysis method should also be applicable to completely deterministic trajectory simulations which however exhibit ergodic behavior in individual trajectories. In addition to first-order coefficients, we also used the stochastic sensitivity analysis method to compute higher order coefficients (selected second and third order) and derived sensitivity coefficients. We have applied both the coupled solution and stochastic sensitivity analysis method to the Ar–Pt (111) scattering system, where we found that the surface corrugation and the steepness of the respulsive two-body interactions were essential features of the interaction potential in determining the quantity of energy transfered.

Notes: The powder Raman spectra and the polarized infrared absorption spectra of a polycrystalline oriented film of (1:1) CT complex of 5,10-dihydro-5,10-dimethylphenazine (M2P) with 7,7,8,8-tetracyanoquinodimethane (TCNQ) are reported together with the polarized reflectance infrared spectra of a mosaic of single crystals [(010) crystal face] and the conductivity spectra obtained from a Kramers–Krönig analysis of the reflectance data. The powder Raman and infrared spectra of M2P–TCNQF4 and their temperature dependence (300–15 K) are also presented. The M2P–TCNQ structure is known to be made up of donor–acceptor dimerized mixed stacks. The spectral features related to electron–molecular vibration (e–mv) interaction are successfully interpreted in terms of the dimer model, whose applicability is further validated after its first use in the case of the low temperature phase of tetrathiafulvalene–chloranil complex. The success is testified by the goodfit obtained between experimental and calculated vibronic features of the near and midinfrared spectra. The extracted values of the e–mv coupling constants of TCNQ moiety compare well with those obtained from other TCNQ complexes, whereas those of M2P are a first informative evaluation. The value of the degree of ionicity of M2P–TCNQ ( ρ=0.5±0.1) is obtained by completing the assignment of the spectra in terms of fundamental vibrational modes normally active under the molecular symmetry of the component molecules and by using carefully chosen diagnostic infrared frequencies. Results show that M2P–TCNQ is definitely one of the still rare cases of mixed stack CT complexes with intermediate ionicity. By using analogous criteria, the interpretation of room temperature and low temperature (15 K) spectra of M2P–TCNQF4 leads to the conclusion that for this complex ρ∼1.0. Its temperature dependent phase transition (T=120 K) between the room temperature regular mixed stack and the low temperature dimerized one is well characterized. The vibronic features appearing in the low-temperature infrared spectrum agree with predictions by the dimer model for a distorted stack. Consequently, it is likely that the phase transition is attributable to a dimerization of the stack due to a Spin–Peierls instability, in agreement with the previous indication given by magnetic susceptibility measurements.

Notes: The model of a classical one-component plasma in the vicinity of a metallic hard wall is shown to be a limiting case of an ideally polarizable interface.

Notes: We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions.

Notes: Molecular dynamics simulation was performed on barium meta-fluorozirconate, BaZrF6, glass by using the Born–Mayer–Huggins pair potential. The cumulative F coordination numbers and the F correlation functions of Zr and Ba ions revealed that, in the simulated BaZrF6 glass, the number and the mean distance of the nearest neighboring F were about eight at 2.12 A(ring) for Zr ions and about ten at 2.75 A(ring) for Ba ions. This is consistent with the previous x-ray diffraction result of the glass. A little uncertainty of the cumulative coordination number, however, may admit the presence of small amounts of seven F-coordinated Zr, as deduced in the previous studies. On the other hand, the Zr–Zr pair correlation function disclosed that the F polyhedra of Zr are linked by sharing the edges and/or the corners, the edge-sharing/corner-sharing ratio in number being approximately 3:2. The glass transition temperature and the Zr–F symmetric stretching vibration spectrum generated for the simulated glass were favorably compared with the observed ones. The mean square displacements and the trajectories of F, Zr, and Ba ions clearly showed that fluorozirconate glasses might exhibit fluoride-ion conduction. The present successful simulation indicates the validity of the calculation procedure, especially of the evaluation of the repulsive parameters of Zr and Ba ions. Based on the previous Raman spectroscopy, differential thermal analysis, and x-ray diffraction studies and the present study, the overall structure of BaZrF6 may be described as follows: In BaZrF6 glass, most of Zr ions are dodecahedrally coordinated by eight F and a small amount of them, monocapped-trigonal prismatically by seven F. These polyhedra connect with each other by sharing the edges and/or corners to build up three-dimensional fluorozirconate network. Ba ions are present as the modifier ions in the interstices of the fluorozirconate network, being surrounded on the average by ten F.

Notes: Strontium nitrite monohydrate [Sr(NO2)2⋅H2O] has been studied at 294, 100, and 20 K by neutron diffraction. Integrated intensities of 2958 (294 K), 4239 (100 K), and 2154 (20 K) reflections were measured at the Brookhaven National Laboratory high flux beam reactor, resulting in 2068 (294 K), 2030 (100 K), and 1934 (20 K) independent structure factors. Structural refinement in monoclinic space group P21 led to R(F)=0.029 (294 K), 0.019 (100 K), and 0.034 (20 K). Lattice constants at 295 K are a=12.5831(4), b=8.94941(15), c=4.4860(2) A(ring), β=99.111(4)°; at 100 K, a=12.539(2), b=8.909(1), c=4.475(1) A(ring), β=99.086(20)°; and at 20 K, a=12.542(2), b=8.901(1), c=4.472(1) A(ring), β=99.030(20)°.The expansivity of all four lattice parameters is nonlinear, with α1=32.8×10−6 K−1, β1=76×10−9 K−2; α2=31.6×10−6 K−1, β2=44×10−9 K−2; α3=15.6×10−6 K−1, β3=15×10−9 K−2; α4=−2.8×10−6 K−1, β4=−21×10−9 K−2 for αTi =α295i [1+αiΔT+βi(ΔT)2], ΔT=T−295 K. The mean-square amplitude of Sr varies linearly with temperature between 20 and 294 K, and extrapolates to a zero-point value of 0.0010(2) A(ring)2. A survey shows that atoms with masses greater than about 80 have similar zero-point amplitudes which increase toward the maximum exhibited by H, with its zero-point amplitude of about 0.023 A(ring)2, as the atomic mass decreases. The coordination (9 and 10) of the two independent Sr2+ ions remains unchanged with temperature: the coordination shell radius decreases on average by 0.012 A(ring) from 294 to 20 K. Comparison with previous x-ray structural results on Sr(NO2)2⋅H2O shows the latter are influenced by scattering from the nitrogen atom lone-electron pair. Small but significant differences in N–O distances among the four independent NO−2 ions are detected at 294 K (0.020 A(ring)) and at 20 K (0.017 A(ring)). The mean N–O distance at 20 K for all four ions is identical at 1.253–1.254 A(ring). The maximum atomic displacement between 294 and 20 K is that by a nitrite ion oxygen, of 0.045 A(ring).

Notes: Recent experiments have shown that porous filters preadsorbed with polymer molecules exhibit an anomalously high pressure drop at high rates of flow. We have modeled the adsorbed polymers as dynamical systems and have found that the introduction of hydrodynamic interaction between molecules destabilizes at a high applied shear. As a direct result this instability will cause the molecules to unravel and stretch far into the cross section of the pore, and thus by inference, cause the observed anomalously high pressure drop. Although much of this paper is devoted to the stability characteristics of the deterministic system, Brownian motion is also considered, and an account of the statistics of the Brownian system when the deterministic system becomes unstable is given. The examples revealed in this paper are not of sufficient complexity to calculate with any accuracy the magnitude of this anomalous pressure drop. We simply present a procedure by which a large variety of more complex models could be undertaken and their ultimate effect clearly understood.

Notes: The equilibrium geometries of the lowest three triplet states of trans glyoxal (HCOHCO) have been predicted at the self-consistent-field (SCF) level of theory using a double zeta plus polarization (DZ+P) basis set, designated C,O(9s5p1d/4s2p1d), H(4s1p/2s1p). Two of the molecular structures thus predicted differ radically from the known 1Ag ground state equilibrium geometry. The predicted relative energies of the three triplet states are notably altered when the effects of electron correlation are treated theoretically. Using configuration interaction (CI) including single and double excitations, the predicted adiabatic excitation energies are 23 000 (a˜ 3Au n→π*), 31 000 (3Bg n→π*), and 31 000 cm−1 (3Bu π→π*), when corrected for unlinked cluster effects.

Notes: The application of the sudden approximation in the derivation of a quantal generalized master equation (GME) is examined. Two different types of physical systems are considered. One is a composite system comprised of a fast primary system and slow bath compared to the time the former is coupled to the latter. The other is a composite system comprised of a slow primary system and fast bath. The resulting sudden GME's for both cases contain non-Markovian memory kernels. In the second case, the memory kernel can be further approximated by a Markovian form. The resulting Markovian-sudden GME is identical to the GME obtained by using the adiabatic elimination method for removing the (fast) stochastic bath coordinates. Using a representation of the Schrödinger propagator for the density operator analogous to the recently developed (energy) sudden representation of the Schrödinger propagator for the wave function, the exact GME is recast into a form such that when the memory kernel and the inhomogeneity term of the equation are expanded in a perturbation series, the zeroth order equation is in the sudden approximation form. Finally, a harmonic oscillator coupled linearly to a bath of harmonic oscillators is used as an illustration. The behavior of the bath correlation functions in the Markovian and the sudden limits is examined. The reduction of the exact GME to the sudden approximation form is also considered.

Notes: Calculations are carried out of the rotational–vibrational energy levels of H2O and D2O for J≤10 by a variational method. The full Watson Hamiltonian is employed, with the potential function in valence displacement coordinates and with the integrations over normal coordinates carried out by Gauss–Hermite quadrature. The basis set consists of products of vibrational functions and symmetric top functions; the vibrational functions diagonalize the Hamiltonian for J=0. Comparison is made with experiment, and also results obtained with different force fields are compared. The mixing of different vibrational functions into a wave function for a given rotational–vibrational state is studied; mixing is found to be quite prevalent.

Notes: The liquid–vapor interface above mixtures of isopropanol (i-C3H7OH) and perfluoromethylcyclohexane (C7F14) has been studied in the vicinity of the consolute point (Tc=363 K). As three-phase coexistence is approached, the excess fluorocarbon adsorbed at this interface increases; the adsorption is expected to diverge at Tc for a mixture of the critical composition. A simple model of the interface which incorporates the adsorption anomaly is compared with our ellipticity measurements. Both the model and our data yield ellipticities which have a finite maximum at 0.1 K above Tc. (In general, the ellipticity is not a monotonic function of the adsorption.) The calculation of the ellipticity uses an exact numerical integration of Maxwell's equations for a model dielectric constant vs height profile. The model dielectric constant profile for the critical composition is consistent with a short-ranged density vs height profile between the vapor and the liquid mixture as well as a much longer ranged composition vs height profile expected at a boundary of a mixture near its consolute point. The liquid–vapor correlation length (0.6 nm) was estimated from the ellipticity data far from Tc. The correlation length for the composition profile was found by combining our interfacial tension data taken below Tc with a compilation based on two-scale-factor universality. Ellipticity data for noncritical compositions are presented; however, their analysis will be presented elsewhere.

Notes: A generalized transformation is applied to a model Hamiltonian incorporating both local and nonlocal exciton–phonon coupling. For the application of the usual transport theory, the difference between the transformed coupling and its thermal average over the free phonon ensemble must be small. This is achieved by a temperature-dependent set of transformation coefficients defined by a transcendental equation which is soluble numerically after some approximation. Nonlocal coupling increases both the exciton binding energy and the usual band narrowing, but it also changes the band shape in a way which may introduce new minima and band broadening. The exciton velocities are then no longer related to the exciton hopping and scattering rates in the same way as in local coupling.

Notes: The transition probabilities for Hydrogen B 2pσ1Σ+u (v′=32–35)←X 1Σ+g (v″=0), C 2pπ1Πu (v′=11–13)←X (v″=0), and B′ 3pσ1Σ+u (v′=5–8)←X (v″=0) were measured using synchrotron radiation in order to investigate the variation of the transition probabilities in the region of the dissociation threshold. The experimental data which agree with calculated probabilities indicate that B′ and C state continua may be of comparable intensities.

Notes: The infrared spectra of ND3⋅D2O and hydrogen or deuterium impurity in NH3⋅H2O or ND3⋅D2O at 100 K are reported for the first time. Their interpretation is aided by a D2h pseudosymmetry caused by the heavy atoms being nearly coplanar in the P212121, D42, crystal. No evidence of the possible disorder of the hydrogen atoms is observed. Oriented gas model calculations gave the approximate relative intensities of the unit cell components of the molecular vibrations. The site splitting and correlation splitting are comparable for ν3 and, probably, ν4 of ammonia; three unit cell components are observed instead of the six predicted under D2, three components being calculated to have near-zero intensity. The symmetric deformation of ammonia, ν2, yields two unit cell modes with significant intensity, separated by 37 cm−1 for NH3 and 23 cm−1 for ND3. The isotope frequency ratio for ν2 is lower thanfor any other mode, so this large splitting must be due to intermolecular coupling, probably transition dipolar in origin. The two strong νOH (HDO) absorptions are 140 cm−1 further apart than the two strong νOH (H2O) absorptions, a surprising result because intramolecular coupling is negligible because νO–H⋅⋅⋅N is ∼400 cm−1 below νO–H⋅⋅⋅O. In contrast, νOD (D2O) yields four strong absorptions approximately centered with respect to the two strong νOD (HDO) absorptions. The O–D⋅⋅⋅N doublet is due to the B1 and B2 unit cell group components, the B3 component being too weak to see, as is the case for ν2 of ammonia. The corresponding O–H⋅⋅⋅N doublet is unresolved. Use of the O–D⋅⋅⋅O–D'interaction force constant of the ice phases, −0.10 mdyn A(ring)−1, and oriented gas model calculations of the relative intensities shows that the O–D⋅⋅⋅O bands at 2390 and 2459 cm−1 are due to the in-phase (B3) and out-of-phase (B2) motions of the two O–D bonds in each chain of water molecules in each unit cell. In NH3⋅H2O the out-of-phase O–H⋅⋅⋅O vibration interacts, probably with 2ν4 of ammonia, and its intensity is dissipated among several weak features. We are unable to explain the difference between the coupled and uncoupled O–H⋅⋅⋅N frequencies, 2887 and 2825 cm−1, in NH3⋅H2O. The bending mode of water is tentatively assigned at 1696, 1467, and 1243 cm−1 for H2O, HOD, and D2O, respectively. The lattice absorptions are assigned to rotational or translational motion. The rotational modes of ammonia are assigned to the B1, B2, and B3 unit cell modes that have significant intensity.

Notes: The microwave spectrum of 3,3,3-trifluoro-2-methylpropene, H2C=C(CH3)CF3 has been recorded from 18.5 to 39.0 GHz. Only a-type transitions were observed and R-branch assignments have been made for the ground vibrational state as well as for three vibrational excited states of the CF3 torsion and one excited state of the CH3 torsion. The rotational constants for the ground vibrational state were found to have the following values: A=3549.25±0.35, B=2465.82±0.05, and C=1978.25±0.02 MHz. The dipole moment components were determined from the Stark effect to be ||μa||=2.44±0.01, ||μb||=0.59±0.09, and ||μt||=2.51±0.03 D. From an analysis of the internal rotational splittings, the threefold barrier for the methyl group was found to be 603±19 cm−1 (1.72 kcal/mol). This value is consistent with the value of 610±4 cm−1 (1.74 kcal/mol) obtained from the far infrared spectrum where the fundamental was assigned at 160.9 cm−1, but only if kinetic coupling between the perfluoromethyl and methyl torsion is taken into account. The CF3 torsional mode was observed at 55.9 cm−1 from which a threefold periodic barrier of 743±7 cm−1 (2.12 kcal/mol) was calculated. No appreciable potential coupling was found between the two C3v rotors. The infrared (3500 to 30 cm−1) and Raman spectra (3500 to 10 cm−1) have been recorded for both the gas and solid states. Additionally, the Raman spectrum of the liquid was recorded and qualitative depolarization values were obtained. All of the normal modes have been assigned based on band contours, depolarization values, and group frequencies. These results are compared to the corresponding quantities in some similar molecules.

Notes: A theoretical study of the spin-orbit autoionization in molecules with 2Π state ion cores is presented. The multichannel quantum defect theory is used with an ab initio calculation of the relevant electronic quantities. In the application to the HI photoionization spectrum the energy positions of the observed resonances between the 2Π1/2 and 2Π3/2 ionization thresholds are well reproduced. The importance of the l mixing especially for the π3σ channels is stressed. An attempt to include the S-uncoupling part of the rotational operator in the calculations gives rise to additional autoionization peaks, associated with a new type of rotational autoionization specific to 2Π-state cores. Theoretical predictions are also made for the angular distribution and spin polarization parameters of the photoelectron in the 1155–1168 A(ring) energy range.

Notes: Canonical variational transition state theory calculations have been performed for the reaction H+CH3→CH4 on potential energy surfaces based on ab initio calculations. Most vibrations were treated as harmonic. The resulting energy levels and partition functions were compared to empirical rules. For the two rotational degrees of freedom (χ) of CH3 which become bending vibrations in CH4, changing from a harmonic oscillator treatment to a hindered rotor treatment changed the partition functions by an order of magnitude or more for C ⋅ ⋅ ⋅ H distances, R, greater than 0.3 nm. The variation of potential energy with R was taken as a standard Morse function, as a stiff Morse function with a variable parameter β or as a Lippincott function. The value of R for which the rate was minimum was found to vary between 0.25 and 0.5 nm, depending on the temperature and the assumed variation of potential energy with R and χ. Provided the χ bending modes were treated as hindered rotations for large values of R, the limiting values of the rate coefficients were similar to the results of experiments, of classical trajectory calculations, and of a modified version of simple collision theory.

Notes: A new method of analysis for the ultrasonic absorption of systems involving multiple coupled equilibria is described. The method consists of calculating the relaxation frequencies and amplitudes under a postulated reaction mechanism using trial values of the rate constants and volume changes and of comparing the computed absorption α/f2 (absorption coefficient over frequency squared) directly with the experimental one. Application of this method to the ultrasonic absorption study of aqueous zinc(II)-thiocyanate solutions reveals that the relaxation absorption is ascribed to the successive complex formation equilibria Zn(SCN)3−nn−1 +SCN−(kn(arrow-right-and-left)k−n)Zn(SCN)2−nn, n=1–4. The rate constants and volume changes of the above reactions are determined. The method proves to be especially effective when the absorption spectra are associated with multiple coupled equilibria and accordingly too broad to be separated to discrete relaxation processes by the usual method of analysis.

Notes: An extension of Huizinaga's model potential method is presented and applied to the study of the equilibrium geometry of the ground electronic state of ScO. In the extended model potential method (EMP) the exchange interaction between the outer core and valence shells are handled more efficiently than in the standard MP method; furthermore, the long range behavior of the model potential is now independent on the reduction of the valence basis set. Using the new method, agreement with all electron results can be achieved in the difficult case of ScO molecule within 0.01 A(ring) in Re, 20 cm−1 in ωe, 0.1–0.2 eV in the binding energy, and an order of 10−3 a.u. in the valence orbital energies.

Notes: Deuterium quadrupole coupling constants were obtained for 39 sites from ab initio SCF calculations. An accuracy comparable to the experimental one is reached with a moderately large basis set of very high local quality. Comparison with experiment shows that electron correlation does not contribute substantially to this property. The experimental values for DNCO and DFCO should be reexamined, the value for CD3Cl in the literature was not properly transformed to the bond axes system, and the experimental value for ND3 agrees with the calculated one, thus showing that a dynamical model is not necessary. Several empirical relations are presented, and a simple classical model is proposed which relates the deuterium quadrupole coupling constant to the bond length with high accuracy. A theoretical study of the HCOOH dimer gives some insight into the importance of different mechanisms which lower the quadrupole coupling constant in the solid.

Notes: The configuration interaction, Möller–Plesset perturbation theory, and coupled-cluster procedures are utilized to determine the dissociation energies, vibrational frequencies, and bond lengths of CuH and Cu2. Good agreement is found between the theoretical and experimental values for these properties. Triple and quadruple excitations and the inclusion of diffuse f functions in the basis set are found to be important for quantitative predictions. A CCD+ST(CCD) approximation, in which the contributions of single and triple excitations are evaluated using the coupled-cluster doubles (CCD) wave function, is found to give a value of De(Cu2) within 0.1 eV of the experimental value when a correction for a relativistic effects is included.

Notes: We present a new Green's function Monte Carlo method for solving for the ground state of the Schrödinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium-like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.

Notes: The dynamics of tunneling of an asymmetric double well interacting with a heat bath is reexamined in the binary collision dilute gas phase limit and investigated in the harmonic bath case. (a) In both cases dynamic and static asymmetries are additive. (b) In both cases, when the tunneling amplitude is not renormalized to a value of zero, the effect of asymmetry on the approach to equilibrium due to incoherent tunneling only quantitatively differs from the symmetric double well. (c) When the renormalized tunneling amplitude is zero, the asymmetric tunneling turns dephasing into population relaxation. (d) Variational methods again give results in agreement with renormalization group and instanton calculations.

Notes: The calculation of the effective electrical conductivity σ* of a dilute dispersion of equisized spheres of radius R distributed with arbitrary degree of penetrability is considered. It is demonstrated that σ*, through second order in the inclusion volume fraction φ2, can be written in terms of the zero-density limits of the pair-connectedness and pair-blocking functions, and certain polarizability tensors which involve one and two inclusions. Rigorous upper and lower bounds on σ*, through order φ22, are shown to depend upon, among other quantities, the aforementioned pair distribution functions and are evaluated for two models: an interpenetrable-sphere model and a certain sphere distribution in which the minimum distance between sphere centers is greater than or equal to 2R. An approximate expression obtained for the low-density expansion of σ* for dispersions of penetrable spheres always lies between the derived bounds on σ*. The study demonstrates that the effect of connectivity of the inclusion phase on σ*, through second order in φ2, can be substantial relative to the conductivity of dispersions of spheres characterized by a pair-connectedness function that is zero for all sphere separations.

Notes: The shapes of two-dimensional linear and ring polymers, with and without excluded volume, are investigated by determining the ratios of the two principal orthogonal components of the mean-square radius of gyration. It is found that ring chains are more symmetrical than linear ones.

Notes: The rotational state distributions of NO molecules scattered at clean and oxidized Ge surfaces were determined by means of laser induced fluorescence (LIF). For low incident kinetic energies (Ekin(approximately-less-than)200 meV) scattering is dominated by trapping/desorption and the molecules coming off the surface are translationally accommodated to the surface temperature. The rotational state populations can in this case be approximated by a Boltzmann distribution. The rotational temperature Trot equals the surface temperature Ts, however only up to about 250 K. Further increase of Ts leads to a leveling off of Trot until a limiting value Trot,lim(approximate)400 K is reached. (Rotational cooling in desorption.) At higher kinetic energies direct-inelastic scattering dominates, and for Ekin=820 meV a pronounced non-Boltzmann distribution (rotational rainbow) is observed. The observed effects are qualitatively interpreted in terms of current theoretical models.

Notes: MTGLE and Langevin equation stochastic classical trajectory studies of the mobile silver cation channeling and activated barrier crossing processes which underly superionic conduction in α-AgI are presented. To interpret non-Kramers effects on the channeling kinetics, a new description of the condensed phase effect on activated barrier crossing is developed. This picture emphasizes the competition between "whipback'' of the reaction coordinate, arising from instantaneous environmental restoring forces, and frequency-dependent dissipation of reaction coordinate energy due to environmental relaxation. The simulations show that while the roughest features of the channeling trajectories are determined by the cation friction coefficient the finer details are governed by short-time scale cation-cage correlations. Analogously, for α-AgI, the gross features of the kinetics, e.g., the rough extent of the breakdown of the transition state model, are described by a Kramers-like picture. The finer details of the kinetics, however, are governed by the competition between whipback, which makes realistic barrier crossing less efficient than Kramers model barrier crossing, and dissipation, which works in the opposite direction.

Notes: The gaseous molecule EuTiO3 has been investigated in a high temperature mass spectrometric study of vapors over the europium–titanium–oxygen system. From the enthalpy of reaction: EuTiO3(g)=EuO(g)+TiO2(g) and proper ancillary data, the atomization energy of this molecule has been determined. In addition, from the study of the gaseous exchange reaction: TiO2(g)+Eu(g)=TiO(g)+EuO(g) the dissociation energy of TiO2(g) has been derived and compared with previous results. The dissociation energies proposed are: D(open circle)0,at(EuTiO3) =2278±28 kJ mol−1 and D(open circle)0,at(TiO2) =1260±12 kJ mol−1.

Notes: Free-ion and crystal-field energy parameters for trivalent lanthanide ions (Ln3+) in Cs2NaLnCl6 and Cs2NaYCl6 are presented and discussed. Spin-correlated crystal-field parameters are determined for those systems for which sufficient data are available. The superposition model is used to compare the crystal-field interactions in the Cs2NaYCl6:Ln3+ and LaCl3:Ln3+ systems.

Notes: Hönl–London factors for 2Σ–2Π transitions in the NO molecule have been measured for the first time, using single photon vacuum UV excitation of the A 2Σ+ and of the D 2Σ+ state. The measured and the calculated line intensities in the subsequent fluorescence are found to be in very good agreement for all 12 branches. The J dependence of the relative line intensities clearly reveals the transition from Hund's coupling case (a) to case (b) for the 2Π ground state.

Notes: Vibrationally highly excited azulene molecules in the electronic ground state (excitation energy 〈E〉=30 600 cm−1) were produced by excitation with a N2 laser. The stepwise deactivation of the excited molecules in collisions with a variety of 23 inert bath gases was monitored by time-resolved hot UV absorption spectroscopy at 290 nm. Using previously determined calibration curves of the absorption coefficient at 290 nm as a function of the excitation energy 〈E〉, energy-loss curves 〈E(t)〉 were recorded and analyzed with respect to the average energies 〈ΔE〉 transferred per collision. The dependencies of 〈ΔE〉 on the excitation energy 〈E〉 were derived. In most cases, 〈ΔE〉 was found to be only weakly dependent on 〈E〉 above 10 000 cm−1, whereas a stronger rise with energy became apparent only at lower energies. A comparison with earlier IR emission experiments on the azulene system is given.

Notes: Vibrational quenching rate constants have been measured for NO+(v) ions in collision with 17 neutral molecules. The dependence of the quenching rate constants on collision energy have been determined from near thermal energy up to ∼ 1 eV in some of these cases. The experimental results can be satisfactorily interpreted using a model of complex formation followed by vibrational predissociation with a rate constant of the order of 109–1010 s−1.

Notes: Measurements of the equilibria (1): A−+B=A+B− with a pulsed electron high pressure mass spectrometer lead to ΔG01, ΔH01, and ΔS01. Equilibria involving SF6 as A and perfluoromethylcyclohexane C7F14 provide electron affinities E.A.(SF6)=1.05±0.1 eV and E.A.(C7F14)=1.06±0.15 eV. The kinetics of reactions (1) involving the above two compounds were studied. The rate constants kf for SF−6 +B=SF6+B− were found to increase with exothermicity of the reaction. The temperature dependence for kf was determined. B compounds leading to high exothermicities were associated with kf at the collision limit and essentially no temperature dependence. B of progressively lower electron affinity led to kf below the collision limit and negative temperature dependence, while B with the lowest E.A. but still leading to exothermic reaction produced lowest kf with positive temperature dependence. A model is provided explaining the above behavior. The known large change of geometry between SF−6 and SF6 introduces an internal barrier in the reaction coordinate for the reactions (1) involving SF6.

Notes: An investigation of relaxation behavior in the bistable iodate–arsenous acid reaction is presented. Relaxations from the unstable steady state and separatrix to a stable steady state are compared to model predictions. Relaxations from the unstable steady state are analyzed with a linearized model and relaxations from near the separatrix are explained in terms of a computed phase portrait.

Notes: We present ab initio Hartree–Fock and valence effective Hamiltonian (VEH) calculations on polyparaphenylene, polypyrrole, and polythiophene dimers and polymer chains. These polymeric materials are among the most studied compounds in the field of conducting polymers. We examine, as a function of the torsion angle between consecutive rings, the evolution of electronic properties such as ionization potential, bandgap and width of the highest occupied bands and of the carbon–carbon bond length between rings. This investigation is motivated by the fact that many derivatives of these compounds have substituents that lead to an increase of the torsion angle between adjacent rings, as a result of steric interactions. As expected, on going from a coplanar to a perpendicular conformation, the ionization potential and bandgap values increase and the width of the highest occupied bands decreases. This makes it more difficult to ionize or reduce the polymer chains and can result in achieving lower maximum conductivities on doping. However, since the evolution of the electronic properties is found to follow a cosine law (related to the decrease of the overlap between the π orbitals on adjacent rings), the modifications up to a ∼40° torsion angle are not very large. For instance, in all three polymers, the ionization potential value for a 40° torsion angle is about 0.4 eV larger than the coplanar conformation value. Therefore, substituents that lead to torsion angles between consecutive rings smaller than 40° are quite acceptable. Finally we discuss the importance, for the substituted compounds, of the possibility of achieving a coplanar conformation upon doping, in order to permit high intrachain mobilities of charge carriers such as bipolarons.

Notes: We have calculated the differential surface capacitance for two different semiconductors MoSe2(0001) and WSe2(0001), as a function of applied potential, for the condition of degeneracy. The calculated curves are compared with the experimentally measured capacitance for the systems, MoSe2(0001) in propylene carbonate containing 0.1 M LiClO4, for a range of crystal conductivities, and WSe2(0001) in acetonitrile containing 0.2 M (C3H7)4N BF4. As expected the experimental values are significantly lower than the calculated values, since the measured capacitance is the total capacitance for the system which is described by the surface capacitance of the semiconductor in series with the Helmholtz capacitance. Calculations based on this model, using the data for the Helmholtz capacitance for a mercury electrode in the same electrolyte, are shown to be in good agreement with the measured values. The results are discussed with particular reference to the screening distance for the semiconductor surface charge in the degenerate region.

Notes: The recombination/desorption of H2 and the desorption of hydrogen atoms from a Si(111) surface have been investigated using Monte Carlo transition-state theory methods with a biased random walk. Rate coefficients, activation energies, preexponential factors, and angular desorption distributions have been computed for both reaction channels. The distribution of polarization angles for the H2 rotational angular momentum vector is also reported. The potential-energy surface is expressed as the sum of a lattice potential, a lattice–adatom interaction term, and an adatom–adatom interaction. Keating's formulation as given by Weber is used for the lattice potential. A pairwise sum of 60 Morse potentials represents the adatom–lattice term. The adatom–adatom interaction is a Morse function multiplied by a hyperbolic switching function. The potential parameters are adjusted to fit the theoretical data for the Si(111)–H interaction potential and the measured adsorption energy of H2 on Si(111). The surface predicts a barrier of 0.61 eV for H2 adsorption and the existence of an H@B|2 precursor state in the recombination/desorption process. Thermal desorption of hydrogen atoms is predicted to be too slow to be an observable process. The computed activation energies are in good agreement with the experimental data. The calculated preexponential factor for H2 recombination/desorption is a factor of 103 smaller than the measured results. A detailed treatment of a reaction mechanism involving an H*2 precursor intermediate indicates that this difference is due to differences in the surface coverage present in the calculations and in the experiments. In general, the theoretical methods are shown to be well suited for the study of this type of rare-event process.

Notes: Photoelectron spectra of tetramethylsilane, were measured at selected photon energies in the vicinity of the Si 2p edge, using synchrotron radiation. In addition to known valence and core Si 2p bands, three LVV Auger lines (69, 76, and 80 eV electron energy) were observed for the first time. Partial and differential cross sections for the Si 2p band and two of the Auger lines have been measured at several photon energies from the Si 2p onset up to 135 eV. An intense resonance is evident in the Si 2p continuum as well as in the LVV Auger decay channels. Its position, right above threshold, accounts for only a part of the absorption feature. Another maximum, already seen in absorption around 124 eV, may be a shape resonance associated with the Si 2p continuum.

Notes: The linearized form of the transport theory recently developed by West and Lindenberg is used to obtain an approximate equation of motion for the density matrix of an exciton confined to a dimer. The resulting equation has a form which may be readily compared with others derived from both dynamical and phenomenological approaches. Comparisons are made between the equations of motion, optical spectra, and generalized master equation memory functions which result from the theories considered.

Notes: The hydrodynamic radius and intrinsic viscosity of a number of dilute solutions containing lightly sulfonated polystyrene ionomers and its unmodified analog have been measured in both polar and nonpolar solvents. Since these ionic interactions are known to significantly modify the physical properties of a polymer through relatively strong intra- and intermolecular interactions, it is important to examine how the individual chain characteristics of a charged polymer are influenced with changes in solvent quality and sulfonation level. In a polar solvent, such as dimethylsulfoxide, a short and a long correlation time is observed indicative of at least two relaxation processes. The long correlation time is attributed to the translational motion of the entire polymer chain, while the short relaxation process is correlated with the motion of the polystyrene segments situated between ionic groups. This result may be due to the ability of dimethylsulfoxide to dissolve lightly sulfonated polystyrene, but not its nonionic analog. On the contrary, in a relatively nonpolar solvent, such as cyclohexanone, only a single correlation function is noted. Again correlation with viscometric measurements shows that this is entirely due to translational motion of the individual coil. In this particular solvent, both polystyrene and sulfonated polystyrene are soluble. These results are useful as a basis for interpreting similar measurements in the semidilute region where the "universal'' solution characteristics of associating polymers more specifically ionomers, may be observed.

Notes: Diffusion coefficients for thermally activated and tunneling diffusion as well as mean square fluctuation data are presented for 1H, 2H, and 3H on W(110), as functions of coverage θ and temperature. If D is written as D0 e−E/kT for thermally activated diffusion, there are only small isotope effects, consistent with zero point energy differences for E, which increases slightly with coverage. There are dramatic isotope effects in D0, which can be approximated by ke−cM−1/2 at low θ, k and c being constants. It is suggested that this behavior results from the large vibron spacings relative to phonon energies, and that adsorbate induced changes in the surface phonon spectrum of W(110) are responsible for the changes in D0 with θ which are also very substantial. For tunneling diffusion isotope effects are remarkably small. This is rationalized in terms of additive mass corrections resulting from adsorbate–substrate interactions, which make the effective masses of the three isotopes very nearly the same. The variation in Dtunneling with θ is explained in terms of increasing barrier heights and slight decreases in effective mass as θ increases. Differences in the behavior of 1H and 3H on the one hand and 2H on the other in the tunneling regime at θ〉0.6 are tentatively explained in terms of the statistics of the isotopes. The effect of oxygen on tunneling diffusion is also presented and discussed. Mean square fluctuations, proportional to the two-dimensional compressibility of the adlayer show isotope effects, decreasing monotonically with increasing mass. Mixtures were also examined. In the activated regime D0 varies very strongly with composition at total constant θ=0.9, going through minima when the mole fraction of the lighter isotope in each binary mixture is ∼75%. Evidence for phase segregations in the mixtures is also presented: Diffusion and fluctuation results for mixtures are most easily interpreted by assuming complete miscibility of any two isotopes above 133 and below 90 K but segregation into two phases between these temperatures, the two phases coming closest to being pure at 115–118 K.

Notes: The 5D3–5D4 cross relaxation process of Tb3+ in CsCdBr3 has been evaluated by analysis of the decay curves of the 5D3 and 5D4 emission. The temperature dependence of the cross relaxation rate can be explained assuming phonon-assisted processes. The results show that the larger amount of Tb3+ ions is incorporated in pairs into the CsCdBr3 lattice.

Notes: Circular dichroism line shape functions are derived for a system consisting of two excited electronic states coupled to a single harmonic vibrational mode. A microscopic quantum field representation is used to develop the time-dependent one-exciton Green's functions for two different models of optical activity: the one-electron model and the coupled oscillator model. An analytic form of the Green's functions for these models is derived using an approximate diagonalization in the strong coupling limit of a general two-level exciton–phonon Hamiltonian [Friesner and Silbey, J. Chem. Phys. 75, 5630 (1981); Friesner, ibid. 76, 2129 (1982)]. Simulated spectra are presented which demonstrate differences between the coupled oscillator and one-electron mechanisms. Possible applications and extensions of this theory are discussed.

Notes: Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eignestates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon–Heller spectral quantization method.